Abstract
We develop a theory of difference approximations to absorbing boundary conditions for the scalar wave equation in several space dimensions. This generalizes the work of the author described in [8]. The theory is based on a representation of analytical absorbing boundary conditions proven in [8]. These conditions are defined by compositions of first-order, one-dimensional differential operators. Here the operators are discretized individually, and their composition is used as a discretization of the boundary condition. The analysis of stability and reflection properties reduces to separate studies of the individual factors. A representation of the discrete boundary conditions makes it possible to perform the analysis geometrically, with little explicit calculation.
Keywords
MathematicsDiscretizationBoundary value problemScalar (mathematics)Mathematical analysisBoundary (topology)Wave equationRepresentation (politics)Partial differential equationDifferential equationStability (learning theory)Applied mathematicsGeometry
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Publication Info
- Year
- 1987
- Type
- article
- Volume
- 49
- Issue
- 179
- Pages
- 65-90
- Citations
- 483
- Access
- Closed
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Cite This
Robert L. Higdon
(1987).
Numerical absorbing boundary conditions for the wave equation.
Mathematics of Computation
, 49
(179)
, 65-90.
https://doi.org/10.1090/s0025-5718-1987-0890254-1
Identifiers
- DOI
- 10.1090/s0025-5718-1987-0890254-1